Algebra in Kindergarten? Absolutely!

 "Pure mathematics is, in its way, the poetry of logical ideas."

Albert Einstein

 

When you think about algebra you might have memories of sitting in a high school math class, searching for unknown values in linear and quadratic equations. Those long ago math courses may seem far removed from today's kindergarten classrooms but did you know that it is essential for educators to promote algebraic reasoning in early childhood education?

I devoured the most recent issue of Young Children (Volume 77, Number 3), especially the article Promoting Algebraic Reasoning in the Early Years by Lindsey Perry. 

In her work Perry advocates for algebra in early math programs that explore two main ideas: composition and decomposition of numbers and properties of operations. According to Perry (2022) algebraic reasoning "involves seeing and describing patterns and relationships between quantities that may be unknown...which builds upon students' understanding of patterns and relationships with known quantities and values" (pg. 17). Perry posits that if children can observe and describe number relationships they can begin to symbolically represent relationships between numbers. 

Composition and Decomposition of Numbers

When children compose they understand that a number can be put together using its parts (e.g., 5 plus 5 equals 10). Decomposition is the opposite where a number can be broken apart in different ways (e.g., 10 can be broken into 8 and 2 or 7 and 3). When children compose and decompose numbers they understand how to manipulate numbers in different ways, which helps them become flexible when solving calculations. For example mentally adding 68 + 22 can become easier when children realize that the ones values total 10 and then add this to the tens value (10 + 60 + 20). Adding 68 plus 22 is the same as adding 10 plus 60 plus 20 but the second strategy may be easier to mentally calculate for many people.

Properties of Operations

Properties of operations encourage children to work flexibly with numbers in order to recognize and manipulate their relationships. This helps them simply calculations in order to more efficiently and accurately solve them. For example the order of addends (numbers added together) does not matter in order to arrive at a sum. 

a + b = b + a 

6 + 4 = 4 + a therefore a must be 6.

The commutative property applies to addition and multiplication. The order of numbers can be switched and it does not change the answer of the operation.

2 + 7 = 9 and 7 + 2 = 9

4 x 5 = 20 and 5 x 4 = 20

The inversion property states that all integers have an inverse number that when added equal zero. 

3 + (-3) = 0

Although complicated young children can play with inversion when they become interested in, and work flexibly with equations.

3 + 2 - 2 = 3

So how can early childhood educators encourage children to participate in activities that promote early algebra? Here are some simple activities that can be used regularly to build children's confidence, ability and interest in number sense.

Equation Line

 

Provide children with a variety of subitizing cards and math symbols (addition sign, subtraction sign, equal sign). Encourage children to arrange the cards in different ways in order to create equivalencies.

 Make 5 (or 10)

Show children a total number of cubes (starting with 5 and then 10 is helpful). Hide the cubes behind your back and remove some. Show children the remaining number of cubes and encourage them to calculate how many are hiding.

Singing Songs with a Five/Ten Frame

When singing popular songs and finger plays with children (e.g., 5 Little Monkeys, 10 in the Bed) add a five or ten frame as a visual and manipulate the number of counters in the frame to match the number being sang. 

Counting Beads

   

A string of counting beads can easily be made using two colours of wooden beads secured on a pipe cleaner. Encourage children to use these when playing number games or engaging in number talks.

Domino Sort

Provide a mat for children (here a foam shamrock has been used but any shape will work). Write numbers on individual mats. Encourage children to sort dominoes and match their quantities to the mats in order to represent the many different dot arrangements possible for each number.

Roll a Ring

 

Seasonal rings are a fun tool to use in math games. Provide children with dice and encourage them to roll and add (or subtract) the numbers. Children can then wear the corresponding number of rings on their fingers. If two players play the game, they can each roll and wear rings and then compare hands to see who has more or less.

Name Equations

 

We enjoy representing children's names with boxes and encouraging them to think about the number, size and shape of the letters. These boxes are also fun to represent at equations so that children can play with their names and integrate a bit of math into literacy.

Calendar-based Number Talks

Morning message is a great time to encourage a daily number talk. We often represent the date in different ways (e.g., dice faces, dominoes, tallies, frames) and then encourage children to calculate the number by paying careful attention to the representations and operation signs used.

Which One Is Wrong?

 

Another favourite number talk is 'Which One is Wrong'. Different equations are displayed and children are challenged to explore each one using manipulatives (e.g., cubes, bead strings) to find the incorrect one. 

What other activities do you use to help children with early algebra? Let's connect on social media @McLennan1977!

Beautiful Beading

We had some delicate treasures that arrived to the classroom as part of our "Beautiful Stuff" project this week! The children were captivated by the many beautiful beads, buttons, and jewelry that came in the brown paper bags. There is something so rich, so magical about beads and buttons. Perhaps it is because we don't know the story of how they came to be; whose outfit did they fall from, what travels have they had? We love working with them in our classroom. Today we displayed this treasure in baskets at our art area and encouraged the children to explore.

 

They noticed that there were many beautiful colours in the collection; we gave them plates and encouraged them to begin sorting what they saw. Soon the children had designated a colour to themselves and searched the collection for trinkets of that colour. It led to a very rich discussion about how colours have many shades, and depending on how you look at the colour, it might be considered a part of more than one group. For example there was a lively debate about whether a teal button belonged with the green or blue group.

 

Once the children sorted their objects we encouraged them to string them together using clear fishing line. The added challenge of working with such delicate materials is that the children had to persevere with stringing many beads and this helped strengthen their fine motor control.

 

Once the colour strings were finished we displayed them in our art window so they could be illuminated by the sun. They are a gorgeous, happy addition to this spot!

 

We also liked how this activity promoted mathematical thinking; children were using their knowledge of colour to sort the objects accordingly. They were also measuring to see which string was longer and how many times it could be wrapped around the branch.

 

"The only difference between an extraordinary life and an ordinary one is the extraordinary pleasures you find in ordinary things."

 

Veronique Vienne

Holiday Beading

We invited children to practise fine motor skills and perseverance by creating with holiday beads. We saw many little fingers at work, carefully crafting mini wreaths and pretty patterned bracelets.

Promoting Math Language

We again encouraged the children to string objects onto yarn using plastic needles. In an effort to embed math language into the experience we purposely displayed various sizes of beads at the centre. The children quickly realized that not all beads would fit over the needle and this led to an interesting discussion using much math terminology to describe the beads (e.g., big, little, size, measurement). The children also began to sort the beads into piles that did and did not fit the needles. Meaningful math opportunities embedded into playful experiences help children understand and appreciate topics that can sometimes seem abstract in isolation. We love to see meaningful math emerge in our work!

Stringing Beads

Strengthening a child's fine motor skills and pincher grasp are an important part of writing readiness. We placed interesting objects on our art table along with fine wire and the children spent time stringing lengths. 

This was a very challenging activity that required patience and persistence. 

In an effort to represent our children as members of a larger community we displayed their creations together. 

Using frames sends the message to children that their creations are valued. 

Beading Provocation

Beading is a great way to encourage fine motor practice and strengthen little fingers in preparation for future writing activities. 

The children were provided with an assortment of delicate beads today and encouraged to create art with them. 

This was a very challenging activity that required much patience.

Sometimes the beads would slip off the wire and we'd have to persevere and start over again. 

Next time you walk by our classroom check out the beaded branch!